Supernova Remnants in the Local Group I: A model for the radio luminosity function and visibility times of supernova remnants

Supernova remnants (SNRs) in Local Group galaxies offer unique insights into the origin of different types of supernovae. In order to take full advantage of these insights, one must understand the intrinsic and environmental diversity of SNRs in the context of their host galaxies. We introduce a semi-analytic model that reproduces the statistical properties of a radio continuum-selected SNR population, taking into account the detection limits of radio surveys, the range of SN kinetic energies, the measured ISM and stellar mass distribution in the host galaxy from multi-wavelength images and the current understanding of electron acceleration and field amplification in SNR shocks from first-principle kinetic simulations. Applying our model to the SNR population in M33, we reproduce the SNR radio luminosity function with a median SN rate of $\sim 3.1 \times 10^{-3}$ per year and an electron acceleration efficiency, $\epsilon_{\rm{e}} \sim 4.2 \times 10^{-3}$. We predict that the radio visibility times of $\sim 70\%$ of M33 SNRs will be determined by their Sedov-Taylor lifetimes, and correlated with the measured ISM column density, $N_H$ ($t_{\rm{vis}} \propto N_H^{-a}$, with $a \sim 0.33$) while the remaining will have visibility times determined by the detection limit of the radio survey. These observational constraints on the visibility time of SNRs will allow us to use SNR catalogs as `SN surveys' to calculate SN rates and delay time distributions in the Local Group.